An Efficient Multi-Slot Transmission Scheme for Bluetooth Systems Chae Young Lee and Ki Won Sung Dept. of Industrial Engineering, KAIST, 7- Kusung Dong, Yusung Gu, Taejon, Korea {cylee, bestre}@mail.kaist.ac.kr Abstract Bluetooth is an open specification for a technology to enable short-range wireless communications. Bluetooth uses a frequency hopping with a slot length of 62 μs. Each slot corresponds to a packet and multi-slot packets of or slots can be transmitted to enhance the transmission efficiency. However, the use of multi-slot packet may degrade the performance under the high channel error probability. Thus, the length of multi-slot should be adjusted according to the current channel condition. In this paper, we propose an efficient multi-slot transmission scheme which adaptively determines the optimal length of slots for a packet according to the channel error probability. We derive the throughput of a Bluetooth connection and develop the decision criteria and the decision rule which give the optimal length of the multi-slot. Maximum likelihood estimator (MLE) is used to estimate the channel error probability. Keywords Bluetooth,, Multi-slot Packet, Mini-slot Error Probability, and Maximum Likelihood Estimator (MLE) power, small sized, and row cost radio that can be embedded in portable devices such as PDAs, mobile phones, and notebook computers. More detailed review of Bluetooth can be found in [2]. Bluetooth operates in the unlicensed ISM (Industrial, Scientific, and Medical) band at 2.4 GHz. A frequency hop transceiver is applied to combat interference. A set of 79 hop carriers is employed at MHz spacing. The nominal hop duration is 62 μs which coincides with the length of a single slot. Each slot corresponds to a packet and multi-slot packets of or slots can be transmitted to enhance the transmission efficiency. In cases of multi-slot packets, they are sent on a single hop carrier. Figure depicts the multislot transmission. As the length of multi-slot increases, the probability of the packet error increases and the damage by the channel error becomes large. Thus, the use of multi-slot packet may degrade the performance under the high channel error probability. Therefore, the length of multi-slots should be adjusted with the current channel condition.. Introduction Bluetooth [] is an open specification for a technology to enable short-range, point to multi-point wireless communications that operate in an ad-hoc fashion. The objective of the Bluetooth technology is the design of low Fig. Multi-slot Transmission
Since a large number of ad-hoc Bluetooth connections mutual coordination, a Bluetooth connection may experience a dynamic change of channel condition. Moreover, the use of unlicensed ISM band generates another source of interference to the Bluetooth connection. Thus, the estimation of the channel error probability is an important factor for the determination of the optimal length of a multi-slot. However, the estimation of the channel error probability is difficult because multi-slot packets with different lengths are transmitted during a single Bluetooth connection. In Bluetooth, the determination of the length of multislots is performed by the Segmentation and Reassembly (SAR) operation. Simple SAR schemes which enhance the link utilization are proposed in [, 4]. However, the channel error is not considered in these works. In [], the channel error probability is considered with an interpolation method in which packet error probabilities of different packet types are predicted from the error probability of the current packet type. However, the method does not provide an accurate estimator of the packet error probability when the length of packets changes frequently. In this paper, we propose an efficient multi-slot transmission scheme which adaptively determines the optimal length of slots of a packet according to the channel error probability. We first discuss the throughput of a Bluetooth connection, then the decision criteria which gives the optimal length of the multi-slot is developed under the assumption that the channel error probability is known. The channel error probability is then estimated from the past transmission history of each Bluetooth device. The maximum likelihood estimator (MLE) is used to estimate the channel error probability from the history of the multislot errors. Finally, a simple decision rule for the optimal length of the multi-slot is developed from the estimation. The proposed decision rule is suitable for Bluetooth devices which require low power consumption. Simulation experiments show an outstanding performance of the may coexist in the same transmission area without any proposed scheme. 2. of Bluetooth In Bluetooth, the duration of one slot is 62 μs, which corresponds to one hop duration. Multi-slot occupies multiple of one slot duration. However, the actual multislot duration is approximately 20 μs shorter than the respective multiple of the hopping duration to allow for synthesizer re-turning [6]. Since the time required for returning cannot be used for data transmission, the per-slot payload size of slot packet (27 bytes/slot) is smaller than that of slot packet (6 bytes/slot) and slot packet (67.8 bytes/slot). We introduce the concept of mini-slot to take the above aspect into account. The duration of a mini-slot is half of the one slot duration. A multi-slot packet which consists of i slots is assumed to consist of mini-slots. Moreover, the ACK and the NAK is assumed to occupy one mini-slot in this paper. Let us define burst_set(i) to be the set of multi-slot of i slots and an ACK or a NAK. In other words, burst_set(i) consists of mini-slots. We also define p and p as the error probabilities of one mini-slot and a burst_set(i), respectively. Let mini-slots in a burst_set(i), and denote the number of payload be the total number of mini-slots during the transmission period of one burst_set(i). The time required for frequency re-turning is considered as one mini-slot both after the transmission of the payload and the ACK/NAK. Then, it is clear that N p ( i) = and (i) = + 2. Let N b (i) be the number of repeated burst_set(i)s for the transmission of a burst_set(i). It includes the re-transmissions in case of error. Also, let T ( p, i) be the throughput of burst_set(i) with mini-slot error probability Bluetooth is given by N p (i) N t (i) N t p. Then, the throughput of the i
N p ( i) T ( p, i) = =. () N ( i) E[ N ( i)] + 2 E[ N ( i)] t b The transmission of a burst_set(i) is successful only when all mini-slots in the burst_set(i) are successfully transmitted. Thus, is given by p i = (. p i Since N b (i) follows geometric distribution with success probability p ), the throughput becomes ( i b Table Decision criteria for the multi-slot transmission Mini-slot error probability Optimal Burst_set(i) 0 p < 0.04 0.04 p < 0.2 Burst_set() p 0.2. Proposed Multi-slot Transmission Scheme ( )( T ( p, i) = ( + 2). (2) Figure 2 shows the throughput of multi-slot transmission computed by the Equation (2). In the figure, it is clear that the optimal length of the multi-slot which gives the maximum throughput varies according to the mini-slot error probability. Hence, an appropriate burst_set(i) should be selected depending on the channel error probability p. The optimal burst_set(i) crosses at p =0.04 and p =0.2. From the figure, a decision criteria for the multi-slot transmission can be obtained as in Table. Note that minislot error probabilities of 0.04 and 0.2 approximately correspond to bit error rates of. 0 and 8 0, respectively. 0.7 0.6 0. 0.4 0. 0.2 0. 0 4 Burst_set() 0 0.0 0. 0. 0.2 0.2 0. Mini-slot Error Probability Fig.2 of Bluetooth 4 The decision criteria shown in Table is based on the assumption that the mini-slot error probability is known. However, this is not the case in the real world. In the real Bluetooth environment, we can only measure the errors of the burst_sets. Therefore, mini-slot error probability should be estimated from the burst_set error rate. The estimation of the channel error probability is difficult because multi-slot packets with different lengths are transmitted during a single Bluetooth connection. Note that error probability of each burst_set(i) is different even with the same mini-slot error probability due to the different number of mini-slots. Moreover, the requirement of low power consumption for Bluetooth devices needs simple estimation of the error probability. We propose an estimation of the mini-slot error probability from the past transmission history of each Bluetooth device. The maximum likelihood estimator (MLE) is employed for the estimation. Let be the number of transmitted burst_set(i)s used for the history information to estimate the mini-slot error probability. Let F i be the number of failed burst_set(i)s among. Then, the number of failed burst_set(i)s among total transmitted burst_set(i)s follows a binomial distribution with probability. Since the transmission of a burst_set(i) is independent of other burst_set(i)s, the likelihood function of mini-slot error probability p is given as follows: p i N F N F N F L( = p p F F N F ( ) p ( p )
N F F N F ( p p ). () The MLE pˆ of the mini-slot error probability p is the value which maximizes the likelihood function. Therefore pˆ is the solution of the equation (4). If F( 0.04) > 0 Then select burst_set() Else if F( 0.2) < 0 Then select burst_set() Else Then select burst_set() dl( = 0. (4) Fig. Decision Rule for the Multi-slot Transmission dp It can be proved that Equation (4) has a unique solution for 0 < p <. In this paper, a brief sketch of the proof is presented as follows. Let p = x ( 0 < x < ) and consider d ln L(. Let In other cases, burst_set() should be selected because pˆ lies between 0.04 and 0.2. With the decision rule in Figure, the optimal length of multi-slot can easily be obtained. The computation of the proposed decision rule is so simple that it can be operated in any Bluetooth device in real time. the numerator of d ln L( be F(. Then, 4. Simulation Results F ( = 2N + 6N + 0N 2F x 2 6F + x 6 0F + x Note that F( 0) 0 and lim F( =. Furthermore, x df( < 0. Thus F( is a monotonically decreasing function of solution for dl( x. Therefore, = 0 dp 0 < p <. 0 () has a unique Using the decision criteria of Table and the MLE of the mini-slot error probability, we develop a simple decision rule for the multi-slot transmission as in Figure. In the range of 0 < p <, F( is monotonically increasing function, and = 0. Therefore, if F( 0.04) > 0, pˆ is less than 0.04, which means burst_set() gives best performance among burst_set(i)s. In the same way, if F( 0.2) < 0, pˆ exceeds 0.2. Thus we should select burst_set() to obtain the optimal throughput. pˆ F( ˆ Simulation experiments are performed to evaluate the performance of the proposed multi-slot transmission scheme. We consider a piconet which consists of one master and one slave. We assume the packet to be transmitted is generated continuously and generated in downlink (from master to slave) only. In uplink, only ACK or NACK is transmitted without piggybacking. FEC is not used in the experiments. Figure 4 shows simulation results for throughputs of burst_set(i)s by changing mini-slot error probability from 0 to 0.. Note that mini-slot error probability of 0. roughly corresponds to bit error probability of. 0. is fixed to 00 because the proposed scheme shows good performance when 00. The effect of on the throughput is discussed later. From Figure 4, it is clear that each burst_set(i) has its range of the best throughput, burst_set() in 0 p 0.04, burst_set() in 0.04 p 0.2, and burst_set() in p 0.2. The proposed scheme forms the envelop of the maximum throughput throughout the range of the mini-slot error probabilities. It shows that the proposed scheme
selects an appropriate burst_set(i) according to the current channel error probability. The effect of By increasing on the throughput is also investigated. from 20 to 400 while the mini-slot error probability is fixed to 0.2, the throughput is as in Figure. It turns out that the proposed scheme shows good performance when 00. Decision rule for the length of the multi-slot is developed with the estimation. The proposed decision rule is simple enough to be calculated in real time with very small computing power of Bluetooth devices. Simulation experiments show the proposed scheme enhances the throughput of a Bluetooth connection. 0.8 0.7 0.6 0. 0.4 0. 0.2 0. 0 Proposed Scheme Burst_set() 0 0.0 0. 0. 0.2 0.2 0. Mini-slot error probability Fig.4 of each burst_set(i) and the proposed scheme with =00 0.64 0.62 0.6 0.8 0.6 0.4 0.2 0. 0.48 0 00 200 00 400 Ni References [] Bluetooth Special Interest Group, Specification of the Bluetooth System, Version., Volume : Core, http://www.bluetooth.com. [2] J. Haartsen, The Bluetooth Radio System, IEEE Personal Communications, Vol. 7, No., Feb. 2000. [] M. Kalia, D. Bansal, and R. Shorey, Data Scheduling and SAR for Bluetooth MAC, IEEE VTC, Spring, 2000. [4] A. Das, A. Ghose, A. Razdan, H. Saran, and R. Shorey, Enhancing Performance of Asynchronous Data Traffic over the Bluetooth Wireless Ad-hoc Network, IEEE INFOCOM, 200. [] J. Kim, Y. Lim, Y. Kim, and J. S. Ma, An Adaptive Segmentation Scheme for the Bluetooth-based Wireless Channel, IEEE International Conference on Computer Communications and Networks, 200. [6] S. Zurbes, Considerations on Link and System of Bluetooth Networks, IEEE International Symposium on Personal, Indoor, and Mobile Radio Communications, 2000. Fig. Effect of with p=0.2. Conclusion In this paper, we proposed an efficient multi-slot transmission scheme which dynamically determines the optimal length of slots of a packet according to the channel error probability. We derived the throughput of multi-slot transmission and estimate the mini-slot error probability. MLE is used to estimate the mini-slot error probability.